Let A and B two distinct points on the parabola `y^(2)=4x`. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Let P and Q be distinct points on the parabola y^(2) = 2x such that a circle with PQ as diameter passes through the vertex O of the parabola . If P lies in the first quadrant and the area of the triangle OPQ is 3 sqrt(2) , then which of the following is (are) the coordinates of P ?

Let A(3, 0) and B(4, 1) are two points on the parabola y=(x-3)^(2) , find a point on this parabola where its tangent is parallel to the chord AB.

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points A and B , respectively. If the center of the circle through P ,A and B is C , then the angle between P C and the axis of x is

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax . If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then

Two parabola have the same focus. If their directrices are the x-axis and the y-axis respectively, then the slope of their common chord is :

Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C be chosen on the on the arc AOB of the parabola where O is the origin such that the area of DeltaACB is maximum. Then the area (in sq. units) of DeltaACB is :